In this section, we compare UAMP-SBL against the conventional SBL [1]} and the state-of-the-art AMP based SBL algorithm GGAMP-SBL [2]} with estimated noise variance and 3 times of the true noise variance. The vector \(\mathbf {x}\)  is drawn from a Bernoulli-Gaussian distribution with a non-zero probability \(\rho \) . The SNR is defined as \(\text{SNR} \triangleq E\left\Vert  \mathbf { \mathbf {A x}} \right\Vert  ^2/ E\left\Vert  \mathbf { \mathbf {w}} \right\Vert  ^2\) . As a performance benchmark, the support-oracle MMSE bound [2]} is also included. We set \(M=800\) , \(N=1000\)  and blackthe SNR is set to be 60dB, unless it is specified. For UAMP-SBL we set the maximum iteration number \(t_{max}=300\)  (note that there is no inner iteration in UAMP-SBL). GGAMP-SBL is a double loop algorithm, the maximum numbers of E-step and outer iteration are set to be 50 and 1000 respectively. The damping factor for GGAMP-SBL is 0.2 to enhance its robustness against tough measurement matrices. It is noted that the damping factor can be increased to reduce the runtime of GGAMP-SBL but at the cost of reduced robustness.
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